1. Field of the Invention
This invention relates to equalizers for multi carrier signals, to equipment having such equalizers, e.g. modems, corresponding methods of equalizing and methods of offering a communication service over a link having such equalizers, and to equalized signals.
2. Description of the Related Art
Multi-carrier modulation is a well known means of transmitting digital data by splitting that data into fixed-length data “blocks” or “symbols” each having the same number of sub-blocks or bits. Analog transmission of these blocks is carried out using a set of carrier signals. For example, there can be a carrier for each of the sub-blocks in one block. The carriers have frequencies which are equally spaced across the transmission band of the transceiver. The carrier frequencies can be orthogonal or not. One such arrangement is called DMT (Discrete multi-tone). DMT modems transmit data by dividing it into several interleaved bit streams, and using these bit streams to modulate several carriers. DMT is used for examples in DSL (Digital subscriber Line) which enables high speed digital data transport over telephone lines. Some varieties of DSL such as ADSL (Asymmetric Digital Subscriber Line), overlay the carriers on the analogue POTS (Plain Old Telephone Service) service. ADSL is useful so that telephone companies can reuse most of their installed wiring for the introduction of new services. By using DMT (Discrete Multi Tone) modulation, carriers with a higher signal to noise ratio (SNR) are capable of carrying more bits than carriers with a low SNR, enabling higher transmission rates.
A significant limitation in this and any multiple carrier system is intersymbol and inter-carrier interference (ISI-ICI). This is essentially caused by delays in the transmission path which can vary with frequency. Since a typical signal pulse can be regarded as having components at many frequencies, the effect is to spread or “disperse” the pulse in the time domain, and this spreading can cause overlap with neighboring pulses. The average duration of the delays is not the principal issue here, it is the variation or range of the delays, varying with time and frequency for example, which causes the “dispersion” and hence ISI.
A known countermeasure to intersymbol and intercarrier interference due to transmission of the DMT symbols over a channel between multicarrier transmitter and multicarrier receiver involves adding a cyclic extension (CE, also called cyclic prefix, CP) to each DMT symbol. The data rate, however, reduces proportionally to the length of the cyclic prefix that is added to the DMT symbols so that the length of the cyclic extension of DMT symbols is preferably limited. The cyclic prefix should preferable be long enough so that channel delay or spreading of one symbol can be absorbed into the cyclic prefix time period. In this way intersymbol interference can be reduced. If the channel impulse response is longer than the cyclic extension, some ISI will remain.
Another known countermeasure to shorten the channel's impulse response is a time domain equalizer. Time domain equalizers (TEQ) typically contain a set of adaptive taps whose values are set in accordance with a mean square error (MSE) criterion. In a typical receiver as shown in FIG. 1, the TEQ is followed by a serial to parallel converter which also acts to extract the cyclic prefix from the multicarrier symbol to output a non-extended multicarrier symbol. This is applied to a Discrete Fourier Transformer (DFT), typically implemented as a Fast Fourier Transformer (FFT unit) for time to frequency domain conversion, since the FFT (Fast Fourier Transform) algorithm is an efficient way of calculating a DFT. This is followed by a frequency domain equalizer FEQ which typically contains one complex tap per carrier to compensate for each carrier any remaining phase rotation and attenuation due to transmission over the channel. The outputs are fed to a demapper DMAP which decodes the appropriate number of bits from each carrier using a selected constellation scheme, and the bits are converted to a serial stream by parallel to serial convertor P/S.
An improved multicarrier receiver RX known from EP 969 637 A1 is shown schematically in FIG. 2. More details may be found in “Per tone Equalization for DMT-Based systems” by Van Acker et al, IEEE Transactions on communications, Vol. 49 No1 January 2001. Both EP 969 637 and the Van Acker article are incorporated herein by reference. In this case, the TEQ is dispensed with and a time domain equalization is carried out in the frequency domain. The key advantage of this is that it enables different amounts of time domain equalization to be carried out on each of the carriers, i.e. a separation of the equalizing function with frequency. As shown in the figure, the samples of the cyclically extended multicarrier symbol MS, when received by the multicarrier receiver RX′, are converted to parallel form as by the serial to parallel converter S/P. The extended multicarrier symbol MS then is fed to the sliding fast Fourier transformer SLIDING FFT which converts the extended multicarrier symbol MS into the frequency domain by calculating several consecutive Fourier transformations.
A complete calculation of these FFTs would be very computationally intensive. However, a sliding DFT (be it implemented using the FFT algorithm) can be derived from one FFT and difference terms. Therefore, in practice the FFTs are replaced by one full FFT and difference terms, without sacrificing performance. The difference terms are formed as differences between incoming samples that are separated by a distance equal to the FFT size.
The parts of the extended multicarrier symbol MS that are transformed (by the FFTs) all have the length of a non-extended multicarrier symbol, i.e. the Fast Fourier Transform (FFT) size. The sliding fast Fourier transformer SLIDING FFT in this way calculates at most an amount of Fourier transforms equal to the number taps of the tapped delay lines TD1, TD2, . . . , TDN/2 in the per-carrier frequency domain equalizer PC-FEQ, also called a per-tone equalizer. The resulting frequency domain multicarrier symbols are applied to the PC-FEQ where each carrier is equalized by an individual equalizer or tapped delay line. The number of complex taps per tapped delay line does not necessarily have to be the same for each tapped delay line, but could be a maximum of T taps per line. The equalized carriers at the output of the per-carrier frequency domain equalizer PC-FEQ are fed as in FIG. 1 to the demapper DMAP′ and the parallel to serial converter P/S′. There is also mention that the equalizer length can be varied per tone and set to zero for non-used tones, to reduce complexity.
It is known from “Frequency Domain equalization with tone grouping in DMT/ADSL-receivers” by Van Acker et al, 1999 IEEE BNSDOCID:<XP—10373800A_I_>, which is also incorporated herein by reference, to apply the equalisation to groups of tones rather than every tone individually, to reduce the complexity in terms of computational load and memory requirements. For each group the optimal per tone equalizer is computed for the centre tone and reused for the whole group.
A further attempt to improve the performance without unduly increasing complexity is shown in EP1296492 and involves windowing in the receiver to reduce the effect of transitions that would otherwise cause intersymbol and intercarrier interference. It can help to reduce the spectral leakage effects due to the bad spectral containment of the DFT operation. Hence, Radio Frequency Interference (RFI) and crosstalk will only affect a limited number of carriers. This known patent application shows a combination of the benefits of the per-tone equalization and of windowing. Complexity is still a limiting factor, and more so with the advent of ADSL+, a new standard based on ADSL where the number of tones in the downstream band has been doubled (from 256 to 512). The upstream band remains the same of ADSL.
Useful general information on ADSL systems can be found in “ADSL, VDSL, and Multicarrier Modulation, by J. A. C. Bingham, Wiley, 2000.